SALANG, Afghanistan — There is not an ounce of fat on the wiry frame of Abdul Wahid, and no wonder.

After he finishes his morning work shift, he walks 10 miles down mountain trails in northern Afghanistan to the first road, where he catches a bus for the last couple of miles to the teacher training institute in Salang. He walks back up the mountain another 10 miles to get home, arriving well after dark, just in time to rest up for his day job.

In his determination to formally qualify as a teacher, Mr. Wahid, 33, exemplifies many of the gains for Afghan education in recent years. “It’s worth it, because this is my future,” he said.

But he also personifies how far the efforts here have yet to go. Mr. Wahid’s day job is being the principal of the high school in his village, Unamak. Though he has only a high school diploma, he is the best educated teacher that his 800 students have.

It is widely accepted that demand among Afghans for better schooling — and the actual opportunity to attend, particularly for girls — is at its highest point in decades. For Western officials seeking to show a positive legacy from a dozen years of war and heavy investment in Afghanistan, improvements in education have provided welcome news.

But for those who are working to make it happen — local Afghan officials, aid workers, teachers and students — there are concerns that much of the promise of improvement is going unfulfilled, and major problems are going unsolved.

In interviews, they pointed out an abysmal dropout rate, widespread closings of schools in some areas of conflict and a very low level of education for those who do manage to find a seat in a class. Overcrowding is so bad that nearly all schools operate on split shifts, so students get a half-day, and many of them are on three shifts a day, meaning that those students get only three hours of instruction daily. And many children are not in school. Unicef estimated in 2012 that one in two school-age children did not attend at all.

Further, while there has demonstrably been positive and rapid growth in the public school system, there have also been daunting challenges, particularly a lack of capacity to find or train qualified teachers, print enough textbooks or build enough safe schools.

According to statistics compiled by Unicef, only 24 percent of Afghanistan’s teachers are qualified under Afghan law, meaning they completed a two-year training course after high school. In many rural places, there are sometimes teachers with 10th-grade educations teaching 11th and 12th graders.

Forty-five percent of the country’s 13,000 schools operate without usable buildings, under tents or canvas lean-tos, or even just under the branches of a tree; in a country of harsh extremes of climate both in winter and in summer, that means many missed school days.

The Afghan public school system has expanded immensely in recent years, buoyed by extensive international aid — the United States Agency for International Development alone has given $934 million to education programs over the past 12 years, according to the government agency. The education minister, Farouk Wardak, insists that 10.5 million students are enrolled this year, 40 percent of them girls, a huge increase from an estimate of 900,000 enrolled students, almost none of them girls, under Taliban rule in 2001.

Those numbers are widely quoted by Afghan and Western officials as a marker of success, but the claims are seen as unsupportable by many here.

Jennifer Rowell of CARE International, who has been conducting a study of education in Afghanistan, cautions that enrollment numbers are not actual attendance numbers.

And she said that when CARE tried to contact the headmasters of schools around the country, using contact lists kept by the Education Ministry, “half to three-quarters of phone numbers of school masters were missing, or the man we call has not been in the job for years.”

That makes it difficult for the Education Ministry to do any meaningful monitoring of actual school attendance around the country. Beyond initial enrollments, attendance tends to drop off quickly, often within just a few weeks. Only about 10 percent of students make it through to graduation, according to U.S.A.I.D. figures.

Those numbers are even lower for girls, most of whom drop out between sixth and ninth grades, after puberty makes them marriageable in many areas. Female teachers are acutely scarce, and families worry about the safety of sending their daughters to school given continuing threats from the Taliban and resistance from some local elders.

The schools themselves have an incentive to inflate their figures, since their financing, which comes from Kabul, is based on enrollment.

In the eastern province of Khost, bordering Pakistan, Education Ministry documents from Kabul officially list 252,000 students enrolled last year. But in Khost Province’s education department, Kamar Khan Kamran, who works as a recruiter of teachers, said those numbers were wildly inflated. “I think we would hardly be able to enroll 20,000 to 25,000 students this year in the province, though the demand for education is booming rapidly.”

The shortage of teachers is so acute that in many districts the schools are hiring teachers who graduated only from sixth, seventh or eighth grade, Mr. Kamran said, “even though it’s not legal.”

For all of that, even those who warn that establishing quality education in the country is a mission far from accomplished will acknowledge that improvement has been marked over the past decade.

One United Nations official, speaking on the condition of anonymity so as not to anger Afghan officials, noted that while there still was not enough attention paid to the quality of education being provided, “enrollment has been tremendous, very encouraging, particularly for girls.”

S. Ken Yamashita, the head of U.S.A.I.D. in Afghanistan, said that even though reliable statistics are hard to come by in Afghanistan, “what’s absolutely clear is the number of kids in school has gone up, the participation of girls has gone up, and it’s such a huge differential.”

He added, “Education is very much a success in Afghanistan.”

A good example of that success is the Sardar Kabuli High School for Girls, in the capital. It was built for $27 million from the United States — and is still not the most expensive American-financed school. The Ghazi Boys High School in Kabul cost $57 million.

Last year Sardar Kabuli High graduated 290 girls, more than a third of the number of this year’s first-grade enrollments, and half of them passed university entrance exams.

“This school is an example to the whole country,” said the headmistress, Nasrin Sultani. Two years ago, it consisted of 38 tents and students attending in three shifts.

Now its 6,600 students, in two shifts, all have their own desks and no more than two students share one textbook.

In Zamina Stanikzai’s 12th-grade math class, when she asked for a show of hands of girls who want to go to college, all but one of the 40 students’ hands shot up. The one was a younger girl, waiting for her sister to finish classes to take her home.

When the girls were asked how many thought their families would allow them to go to college, however, half of the hands went down.

A girl in the back stood up and asked to speak, which she did in halting but good English. “Many of our families still believe in the old ways,” she said.

Mr. Wardak, the education minister, expressed pride when he talked about what has been accomplished despite the challenges, and particularly in remote areas, like Ghor Province. “For the first time in the 5,000-year history of Afghanistan, for instance, Ghor has 800 schools, 173 of them high schools,” he said in an interview.

He becomes defensive, however, about the quality issue. “I have $70 per student per year to spend,” he said. “In the U.S. you spend $20,000, in Pakistan $130. You don’t expect to do much for $70 a year.”

Outside Kabul’s public school system, the difference in quality can be drastic. At Mir Ali Ahmad Girls School in Char-i-Kor, in Parwan Province, the girls share their building with boys — two shifts for boys, one for girls. Only the boys have sports fields and playgrounds. One set of textbooks is shared by three or four girls. Two girls share a seat at each desk.

And even in the capital, most public schools are not the showpiece that Sardar Kabuli High is.

At Sayid Ismail Balkh School, 8,000 students are enrolled in three shifts, three hours each. They have buildings, but one set of them has no roofs or windows — it was a World Bank project, but the contractor took the money and ran — and another set was a Japanese-financed project that also was never finished, so only the first of two stories were built. Canvas tarps are slung over the walls to provide shelter.

“When it rains, we take the day off,” said Barat Ali Sadaqi, the headmaster.

Toilet facilities and running water systems have not been finished, and the odor of sewage permeates the small compound. Electricity is intermittent, and there are six computers for the whole student body.

On a given day, only 5,400 students attend out of the 8,000 enrolled. Still, they are crammed in: three to a desk, 40 to a class, 10 textbooks per class.

“This is development after 10 years in Kabul,” Mr. Sadaqi said.

A version of this article appears in print on , Section A, Page 1 of the New York edition with the headline: Despite Education Advances, A Host of Afghan School Woes. Order Reprints | Today’s Paper | Subscribe